Subject: Geometry

# Words & Symbols In Geometry

## Geometry.WordsAndSymbols History

Hide minor edits - Show changes to output

December 26, 2010
by -

Changed line 92 from:

(:cellnr:)'+{$ \~~begin~~{~~matrix}~~\rightarrow~~\\ ~~AB ~~\end{matrix}~~$}+'

to:

(:cellnr:)'+{$ \overset{\rightarrow}{AB} $}+'

Changed line 94 from:

(:cell:){$ \~~begin~~{~~matrix}~~\rightarrow~~\\ ~~AB~~ \end{matrix~~} $}

to:

(:cell:){$ \overset{\rightarrow}{AB} $}

December 26, 2010
by -

Changed line 124 from:

(:cell:){$\~~overrightarrow~~{AB} = \infty $}

to:

(:cell:){$ \overleftrightarrow{AB} = \infty $}

December 26, 2010
by -

Changed line 92 from:

(:cellnr:)'+{$ \~~overrightarrow~~{~~ab~~} $}+'

to:

(:cellnr:)'+{$ \begin{matrix}\rightarrow\\ AB \end{matrix}$}+'

Changed line 94 from:

(:cell:){$ \~~overrightarrow~~{~~ab~~} $}

to:

(:cell:){$ \begin{matrix}\rightarrow\\ AB \end{matrix} $}

Changed lines 102-104 from:

(:cell:)a – b = c ∴ c + b = a

to:

(:cell:)a – b = c

∴ c + b = a

∴ c + b = a

Changed line 114 from:

(:cellnr:)'+~~≈~~+'

to:

(:cellnr:)'+{$ \approx $}+'

Changed line 116 from:

(:cell:)a ~~≈~~ ~~x~~

to:

(:cell:)'+{$ a \approx x $}+'

December 26, 2010
by -

Added lines 75-144:

(:table border=1 cellpadding=5 cellspacing=0:)

(:cellnr align=center bgcolor=#d4d7ba:)'''Symbol'''

(:cell align=center bgcolor=#d4d7ba:)'''Name'''

(:cell align=center bgcolor=#d4d7ba:)'''Example'''

(:cell align=center bgcolor=#d4d7ba:)'''Meaning'''

(:cellnr:)'+{$ \Delta $}+'

(:cell:)Triangle

(:cell:)'+{$ \Delta ABC $}+'

(:cell:)The triangle with points A, B and C.

(:cellnr:)'+{$ \angle $}+'

(:cell:)Angle

(:cell:){$ \angle A $}= 23°

(:cell:)Angle A is 23 degrees.

(:cellnr:)'+{$ \overline{AB} $}+'

(:cell:)Line Segment

(:cell:){$ \overline{AB} $} = 2.4 ft

(:cell:)The distance between points A and B is 2.4 feet.

(:cellnr:)'+{$ \overrightarrow{ab} $}+'

(:cell:)Ray

(:cell:){$ \overrightarrow{ab} $}

(:cell:)The line that begins at point A and continues through point B to infinity.

(:cellnr:)'+{$ \overleftrightarrow{AB} $}+'

(:cell:)Line

(:cell:){$ \overleftrightarrow{AB} $}

(:cell:)The infinite line that passes through or has points A and B.

(:cellnr:)'+∴+'

(:cell:)Therefore

(:cell:)a – b = c ∴ c + b = a

(:cell:)a minus b is c, therefore c plus b is equal to a.

(:cellnr:)'+< and >+'

(:cell:)Less/Greater Than

(:cell:)a < b

(:cell:)Length a is smaller than length b.

(:cellnr:)'+≤ and ≥+'

(:cell:)Less/Greater Than Or Equal To

(:cell:)a < b ≥ c

(:cell:)a is smaller than b, b is larger than or equal to c.

(:cellnr:)'+≈+'

(:cell:)Is Almost Equal To

(:cell:)a ≈ x

(:cell:)The difference between a and x is negligible.

(:cellnr:)'+{$ \perp $}+'

(:cell:)Perpendicular To

(:cell:){$ AB \perp BC $}

(:cell:)Line AB is perpendicular to Line BC.

(:cellnr:)'+{$ \infty $}+'

(:cell:)Infinity

(:cell:){$\overrightarrow{AB} = \infty $}

(:cell:)Line AB has infinite length.

(:cellnr:)'+r+'

(:cell:)Radius

(:cell:)r = 16.5

(:cell:)The radius is 16.5 units in length

(:cellnr:)'+d+'

(:cell:)Diameter

(:cell:)d = 50

(:cell:)The diameter is 50 units in length

(:cellnr:)'+⊙+'

(:cell:)Circle

(:cell:)⊙A<⊙B

(:cell:)Circle named A is smaller than Circle named B.

(:cellnr:)'+π+'

(:cell:)Pi (Pronounced ‘pie’)

(:cell:)π = C/D

(:cell:)Pi equals the circumference of a circle divided by that circles diameter.

(:cellnr:)'+{$ \cong $}+'

(:cell:)Congruent To

(:cell:){$ AB \cong BC $}

(:cell:)Lines AB and BC are of equal length, they are congruent to each other.

(:tableend:)

(:cellnr align=center bgcolor=#d4d7ba:)'''Symbol'''

(:cell align=center bgcolor=#d4d7ba:)'''Name'''

(:cell align=center bgcolor=#d4d7ba:)'''Example'''

(:cell align=center bgcolor=#d4d7ba:)'''Meaning'''

(:cellnr:)'+{$ \Delta $}+'

(:cell:)Triangle

(:cell:)'+{$ \Delta ABC $}+'

(:cell:)The triangle with points A, B and C.

(:cellnr:)'+{$ \angle $}+'

(:cell:)Angle

(:cell:){$ \angle A $}= 23°

(:cell:)Angle A is 23 degrees.

(:cellnr:)'+{$ \overline{AB} $}+'

(:cell:)Line Segment

(:cell:){$ \overline{AB} $} = 2.4 ft

(:cell:)The distance between points A and B is 2.4 feet.

(:cellnr:)'+{$ \overrightarrow{ab} $}+'

(:cell:)Ray

(:cell:){$ \overrightarrow{ab} $}

(:cell:)The line that begins at point A and continues through point B to infinity.

(:cellnr:)'+{$ \overleftrightarrow{AB} $}+'

(:cell:)Line

(:cell:){$ \overleftrightarrow{AB} $}

(:cell:)The infinite line that passes through or has points A and B.

(:cellnr:)'+∴+'

(:cell:)Therefore

(:cell:)a – b = c ∴ c + b = a

(:cell:)a minus b is c, therefore c plus b is equal to a.

(:cellnr:)'+< and >+'

(:cell:)Less/Greater Than

(:cell:)a < b

(:cell:)Length a is smaller than length b.

(:cellnr:)'+≤ and ≥+'

(:cell:)Less/Greater Than Or Equal To

(:cell:)a < b ≥ c

(:cell:)a is smaller than b, b is larger than or equal to c.

(:cellnr:)'+≈+'

(:cell:)Is Almost Equal To

(:cell:)a ≈ x

(:cell:)The difference between a and x is negligible.

(:cellnr:)'+{$ \perp $}+'

(:cell:)Perpendicular To

(:cell:){$ AB \perp BC $}

(:cell:)Line AB is perpendicular to Line BC.

(:cellnr:)'+{$ \infty $}+'

(:cell:)Infinity

(:cell:){$\overrightarrow{AB} = \infty $}

(:cell:)Line AB has infinite length.

(:cellnr:)'+r+'

(:cell:)Radius

(:cell:)r = 16.5

(:cell:)The radius is 16.5 units in length

(:cellnr:)'+d+'

(:cell:)Diameter

(:cell:)d = 50

(:cell:)The diameter is 50 units in length

(:cellnr:)'+⊙+'

(:cell:)Circle

(:cell:)⊙A<⊙B

(:cell:)Circle named A is smaller than Circle named B.

(:cellnr:)'+π+'

(:cell:)Pi (Pronounced ‘pie’)

(:cell:)π = C/D

(:cell:)Pi equals the circumference of a circle divided by that circles diameter.

(:cellnr:)'+{$ \cong $}+'

(:cell:)Congruent To

(:cell:){$ AB \cong BC $}

(:cell:)Lines AB and BC are of equal length, they are congruent to each other.

(:tableend:)

December 23, 2010
by -

December 23, 2010
by -

Added lines 1-75:

(:title Words & Symbols In Geometry:)

This section will serve as a basic introduction to some of the things you’ll see in geometry – you’ll no doubt have heard many of these terms and seen many of these symbols before, but it’s good to see what we’ll be using, and it’s handy to have a quick guide.

!!! A List of Words Used in Geometry

''(More in depth explanations and examples will be covered in subsequent pages!)''

(:table border=1 cellpadding=5 cellspacing=0:)

(:cellnr bgcolor=#d4d7ba colspan=14 align=center:) '+'''The Breakdown'''+'

(:cellnr:)

*[[#t1 | Definitions for Points, Lines & Planes]]

*[[#t2 | Definitions for Angles]]

*[[#t3 | Definitions for Circles]]

*[[#t4 | Definitions for Other Geometric Words]]

*[[#t5 | Geometric Symbols]]

(:tableend:)

[[#t1]]

!!POINTS, LINES AND PLANES

:Line: In geometry, the definition of line must be more precise than our everyday use of the word because we also have to deal with rays and segments. A line may be straight or curved, and straight lines continue on past any points upon them. Lines are usually named after their two furthest points.

:Ray: A portion of a straight line that begins at a point and continues indefinitely.

:Segment: A portion of a straight line with two distinct endpoints, a line with finite length.

:Point: A symbol used to show position. Represented by a small dot or a letter.

:Endpoint: A point at one end of a segment, or the beginning of a ray.

:Midpoint: A point exactly halfway along a segment.

:Axis / Axes: A fixed, numbered reference line used in coordinate geometry.

:Origin: The point at which two or more axes meet in coordinate geometry.

:Vertex: The point where two straight lines, segments or rays meet creating an angle.

:Bisect: To bisect is to cross a line or segment at it’s midpoint.

:Plane: A two-dimensional form with length and width but no depth or thickness.

:Collinear: A set of two or more points is said to be collinear if they lie upon the same line.

:Congruent: Segments that have the same length are congruent.

\\

[[#t2]]

!!ANGLES

:Measure: A word used when talking about the value of an angle. An example might be “The measure of angle X is 120°”.

:Right Angle: An angle with a measure of exactly 90°.

:Perpendicular: Two lines are perpendicular if the angle which their intersection or meeting point forms is exactly 90°.

:Obtuse: An angle with measure greater than 90° and less than 180°.

:Acute: An angle with a measure of less than 90°.

:Adjacent Angles: Two angles are adjacent if they share the same vertex.

:Vertical Angles: Two non-adjacent angles formed by intersecting lines.

:Complementary: Angles whose combined total value add to exactly 90°.

:Supplementary: Angles whose combined total value add to exactly 180°.

\\

[[#t3]]

!!CIRCLES

:Chord: A straight line joining any two points on a circle.

:Secant: A straight line joining any two points on a circle and continuing beyond those points in both directions.

:Arc: A portion of the circumference of a circle between and including two points.

:Diameter: A chord that passes through the middle of the circle.

:Radius: The straight length or distance between the centre of a circle and a point on its circumference. The radius of a circle is exactly half of that circles diameter. The plural of radius is radii (pronounced ‘ray-dee-eye’).

:Circumference: The length around a circle.

:Semicircle: An arc measuring exactly half the circumference of a circle. Literally half a circle.

:Central Angle: An angle formed by two radii of the same circle (not two overlapping circles).

:Pi: A constant, irrational number derived from the ratio of the circumference of a circle to its diameter. Pi always has the same value, regardless of the size of a circle. This value has been calculated to many trillions of digits, but 3.141 is fine for our purposes.

\\

[[#t4]]

!!OTHER

:Parallelogram: An enclosed two-dimensional shape wherein all opposing sides are parallel.

:Polygon: An enclosed two-dimensional shape with a finite number of straight sides.

:Quadrilateral: A polygon with exactly four sides.

[[#t5]]

!! A TABLE OF GEOMETRIC SYMBOLS

This section will serve as a basic introduction to some of the things you’ll see in geometry – you’ll no doubt have heard many of these terms and seen many of these symbols before, but it’s good to see what we’ll be using, and it’s handy to have a quick guide.

!!! A List of Words Used in Geometry

''(More in depth explanations and examples will be covered in subsequent pages!)''

(:table border=1 cellpadding=5 cellspacing=0:)

(:cellnr bgcolor=#d4d7ba colspan=14 align=center:) '+'''The Breakdown'''+'

(:cellnr:)

*[[#t1 | Definitions for Points, Lines & Planes]]

*[[#t2 | Definitions for Angles]]

*[[#t3 | Definitions for Circles]]

*[[#t4 | Definitions for Other Geometric Words]]

*[[#t5 | Geometric Symbols]]

(:tableend:)

[[#t1]]

!!POINTS, LINES AND PLANES

:Line: In geometry, the definition of line must be more precise than our everyday use of the word because we also have to deal with rays and segments. A line may be straight or curved, and straight lines continue on past any points upon them. Lines are usually named after their two furthest points.

:Ray: A portion of a straight line that begins at a point and continues indefinitely.

:Segment: A portion of a straight line with two distinct endpoints, a line with finite length.

:Point: A symbol used to show position. Represented by a small dot or a letter.

:Endpoint: A point at one end of a segment, or the beginning of a ray.

:Midpoint: A point exactly halfway along a segment.

:Axis / Axes: A fixed, numbered reference line used in coordinate geometry.

:Origin: The point at which two or more axes meet in coordinate geometry.

:Vertex: The point where two straight lines, segments or rays meet creating an angle.

:Bisect: To bisect is to cross a line or segment at it’s midpoint.

:Plane: A two-dimensional form with length and width but no depth or thickness.

:Collinear: A set of two or more points is said to be collinear if they lie upon the same line.

:Congruent: Segments that have the same length are congruent.

\\

[[#t2]]

!!ANGLES

:Measure: A word used when talking about the value of an angle. An example might be “The measure of angle X is 120°”.

:Right Angle: An angle with a measure of exactly 90°.

:Perpendicular: Two lines are perpendicular if the angle which their intersection or meeting point forms is exactly 90°.

:Obtuse: An angle with measure greater than 90° and less than 180°.

:Acute: An angle with a measure of less than 90°.

:Adjacent Angles: Two angles are adjacent if they share the same vertex.

:Vertical Angles: Two non-adjacent angles formed by intersecting lines.

:Complementary: Angles whose combined total value add to exactly 90°.

:Supplementary: Angles whose combined total value add to exactly 180°.

\\

[[#t3]]

!!CIRCLES

:Chord: A straight line joining any two points on a circle.

:Secant: A straight line joining any two points on a circle and continuing beyond those points in both directions.

:Arc: A portion of the circumference of a circle between and including two points.

:Diameter: A chord that passes through the middle of the circle.

:Radius: The straight length or distance between the centre of a circle and a point on its circumference. The radius of a circle is exactly half of that circles diameter. The plural of radius is radii (pronounced ‘ray-dee-eye’).

:Circumference: The length around a circle.

:Semicircle: An arc measuring exactly half the circumference of a circle. Literally half a circle.

:Central Angle: An angle formed by two radii of the same circle (not two overlapping circles).

:Pi: A constant, irrational number derived from the ratio of the circumference of a circle to its diameter. Pi always has the same value, regardless of the size of a circle. This value has been calculated to many trillions of digits, but 3.141 is fine for our purposes.

\\

[[#t4]]

!!OTHER

:Parallelogram: An enclosed two-dimensional shape wherein all opposing sides are parallel.

:Polygon: An enclosed two-dimensional shape with a finite number of straight sides.

:Quadrilateral: A polygon with exactly four sides.

[[#t5]]

!! A TABLE OF GEOMETRIC SYMBOLS